Abstract
In the wake of a method for detecting Euclidean number fields with the aid of exceptional units, described in 1977 by H. W. Lenstra jr., we study a group action on cliques of exceptional units, determine the corresponding group and exploit the action in some concrete rings. This has also yielded 37 new Euclidean fields in degrees 5, 6, 7, 8, 9, and 10.
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